Tensor Contraction Engine

So Hirata, Tensor contraction engine abstraction and automated parallel implementation of configuration-interaction, coupled-cluster, and many-body perturbation theories. J. Phys. Chem. A 107, 4940 (2003). 

JJ For discussion of the Tensor Contraction Engine see http //www.csc.lsu.edu/gb/TCE/ and the recent publication of S. Hirata entitled Symbolic Algebra in Quantum Chemistry ... 

As a disadvantage, we see particularly the very complex structure of the working equations resulting from these formalisms. This obstacle could be overcome by some automatized implementation tools like the Tensor Contraction Engine (TCE) [35], however, at least some of the methods have also very big computational demands, since solutions for many sectors of the Fock space are required. 

P. Sadayappan, G. Baumgartner, D.E. Bernholdt, R.J. Harrison, S. Hirata, M. Nooijen, R.M. Pitzer and J. Ramanujam The Tensor Contraction Engine, http //www.cse.ohio-state.edu / gb/TCE... 

Although simple models are essential for a fundamental understanding, in the future more realistic models are required, in particular in view of possible applications in cell and tissue engineering. Here we have used cable networks as a first step towards more realistic models for both cell and the matrix. Anisotropic force contraction dipoles are only the first order approximation for the complex mechanical activity of cells and might be extended to more general tensors for mechanical activity and susceptibility. A more sophisticated model would be to replace the force dipoles by whole cell models incorporating the focal adhesion dynamics and stress fibers evolution. 

Note. CN, Contracted notation EN, Engineering notation TN, Tensor notation. 

Contracted notation (CN) has been introduced in the equations, where it is convenient for computer solution to use single-digit subscripts to designate stress and strain terms. The relationships between (1) tensor or elasticity notation, (2) engineering notation (EN), and (3) CN are defined in Table 8.3. 

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